I should warn you that, perhaps, you may be playing your Blue Eyes Twin Burst Dragon incorrectly (as per your "just by having...").
Let's break down the effect of that card:
Must be either Fusion Summoned,
This means that one option to Fusion summon it by using Polymerization, as you correctly pointed out, or...
or Special Summoned by sending the above monsters you control to the Graveyard (in which case you do not use "Polymerization")
instead Special Summon it by sending both Blue Eyes White Dragons to the GY. Do note that you control things that are on your part of the field. Things on hand are not under your control; they are under your possession, though, and you also surely are the owner of that card. These are other two important in-game terms to remember.
and cannot be Special Summoned by other ways.
Meaning no Call of the Haunted, or back from Banish, nor anything similar. If it's dead, its dead (time for Dragon Mirror maybe?).
Under these considerations we can see that if you want to use the Special Summon you must have two Blue-Eyes White Dragon on the field (or at least two cards with that name ;) if you copycat one). This is more restricted as being able to do this from the hand (quite OP to do don't you think?).
Or you can well Fusion summon to be able to use them as materials from your hand or the field (more accessible, but requires Polymerization or similar)
As we can see, either Polymerization or having two Blue Eyes on the field is a "reasonable" requirement to summon such powerful card. Thus, both summon ways balance each other (so it does not become broken).